Interest rate risk of Chinese commercial banks based on the GARCH-EVT model

The paper studies interest rate risk for Chinese commercial banks in the context of China’s completed interest rate liberalization (marketisation). Post-liberalization, market-determined rates have increased volatility and risk exposure for banks operating within a bank-centric financial system. The COVID-19 period and macroeconomic uncertainty further heightened asset price volatility and interest rate fluctuations. The study identifies a gap: despite extensive use of GARCH and EVT models in various markets, limited research focuses on Chinese commercial banks’ interest rate risk using these methods. The research aims to model and predict overnight SHIBOR (O/N SHIBOR) volatility and Value-at-Risk (VaR) to support daily risk management and policy guidance. Research questions: (1) What risks do commercial banks face from interest rate fluctuations? (2) Can a combined GARCH–EVT modeling framework better quantify and minimize such risks? (3) What policies should guide banks under heightened interest rate risk? The hypothesis posits that GARCH–EVT better predicts VaR faced by commercial banks after interest rate marketization.

VaR is a standard tool for quantifying market risk, but estimation accuracy hinges on modeling volatility and tail behavior. Historical simulation is widely used but may fail under extreme volatility. GARCH models effectively capture volatility clustering, yet normality assumptions can underestimate tail risk. Extensions include alternative error distributions (Normal, Student’s t, skewed t, GED/SGED, NIG, α-stable) and asymmetric/long-memory structures (EGARCH, TGARCH/GJR, APARCH, FIGARCH, MNGARCH, HN-GARCH, multivariate BEKK/DCC). EVT addresses tail modeling independent of full return distribution and has been successfully combined with GARCH to estimate tail risk measures. The literature documents GARCH(-EVT) applications across commodities, equities, and cryptocurrencies but has not focused on Chinese commercial banks’ interest rate risk post-liberalization. This study contributes by applying GARCH–EVT to O/N SHIBOR to estimate VaR and by conducting regime analysis. Hypothesis: GARCH–EVT outperforms standard GARCH for extreme (1%) VaR.

Data: O/N SHIBOR daily series from 2015-10-24 to 2021-10-22 (1497 observations). Returns computed as first-order log differences to address non-stationarity and capture financial series’ leptokurtosis. Descriptive statistics and Ljung-Box (LB) tests establish non-randomness and justify GARCH modeling. Regime analysis: A two-state Markov regime switching (MS) model (Hamilton, 1989) identifies low- and high-volatility regimes, estimating transition probabilities via maximum likelihood. The transition matrix P = [[1−p, p],[q, 1−q]] characterizes regime persistence and switching. VaR definition: VaR at confidence level α defined as the α-quantile of the loss distribution. Parametric VaR computed as VaR_α = μ + z_ασ under distributional assumptions. Volatility modeling: Mean equation γ_t = μ + ε_t with AR(1) component selected via ACF/PACF. Conditional variance modeled using: - GARCH(1,1): σ_t^2 = ω + αε_{t−1}^2 + βσ_{t−1}^2. - EGARCH(1,1): ln σ_t^2 = ω + β ln σ_{t−1}^2 + γ |ε_{t−1}|/σ_{t−1} + α ε_{t−1}/σ_{t−1} to capture leverage asymmetry. - TGARCH(1,1): σ_t^2 = ω + αε_{t−1}^2 + βσ_{t−1}^2 + γ ε_{t−1}^2 I(ε_{t−1}<0) to capture asymmetric effects. Error distributions assessed include Normal, skew-normal, Student’s t, skew-t, GED, SGED, and NIG. Model selection uses AIC and parameter significance; residual diagnostics via standardized residual ACF/PACF and LB tests. EVT for tails: Peak-over-threshold (POT) approach with generalized Pareto distribution (GPD) fitted to residual exceedances over threshold μ. GPD parameters (shape ξ, scale β) estimated; left-tail VaR derived using estimated tail parameters and exceedance counts. Backtesting: Out-of-sample VaR forecasts evaluated using Kupiec (1995) unconditional coverage and Christoffersen (1998) independence tests at 1%, 5%, and 10% levels. Rolling-window VaR curves illustrate time-varying risk. Robustness: alternative subsamples re-estimated to check model stability (AIC comparisons).

- Data properties (Table 1): For O/N SHIBOR log-differenced returns (n≈1496 after differencing): mean −0.0001, std. dev. 0.1071, max 1.050, min −0.488, skewness 1.621, kurtosis 14.908. LB tests (levels and squares) significant at 1%, confirming autocorrelation/ARCH effects and suitability for GARCH. - Regime switching (Table 2): Clear transition from prolonged low volatility to high volatility around 2018. Estimated transition probabilities show strong persistence: P11=0.9482 (low→low), P21=0.0518 (high→low), with overall higher likelihood to remain in the current regime; AIC −4642.399. Marketisation is associated with higher SHIBOR volatility. - GARCH-family estimation: Among AR(1)-GARCH(1,1) with multiple distributions, SGED yielded the lowest AIC, but some parameters (ω) lacked significance. Asymmetric models improved fit: EGARCH and TGARCH detected leverage asymmetry (EGARCH parameter indicating stronger reaction to bad news; TGARCH γ significantly >0). The best overall model by AIC is AR(1)-EGARCH(1,1)-GED. High volatility persistence (β≈0.965) indicates strong clustering and slow decay of shocks. - Residual diagnostics: Standardized residuals show no significant autocorrelation; LB tests on residuals and squared residuals are insignificant, indicating adequate fit (white-noise residuals). - One-day VaR (GARCH only, Table 7) under EGARCH-GED: VaR1% = −0.5351, VaR2.5% = −0.3779, VaR5% = −0.2700, VaR10% = −0.1726. - EVT-POT on EGARCH residuals (Figure 3, Table 8): Threshold μ≈1.5853 with N=50 exceedances. Estimated tail parameters: ξ=0.4791 (0.1921), α=0.7289 (0.1667), scale β≈1.5853. EVT-based VaR: VaR1% = −0.6609, VaR2.5% = −0.3453, VaR5% = −0.2135, VaR10% = −0.1340. EVT gives more conservative 1% tail risk than GARCH alone. - Backtesting (Table 9): VaR forecasts pass Kupiec and Christoffersen tests at 1% and 5% significance levels (fail to reject H0), indicating correct coverage and independence; at 10% some tests reject H0, suggesting reduced accuracy at less-extreme quantiles. Rolling-window plots show pronounced time variation; 1% VaR breaches can exceed −2% in extreme periods. - Robustness (Table 10): Across subsamples, EGARCH-GED maintains the lowest AIC among candidates, confirming model stability.

The findings indicate that post-liberalization Chinese interest rates experienced a regime shift to higher volatility, exposing commercial banks to heightened market risk. Modeling results show that incorporating asymmetry and fat tails is crucial: the EGARCH-GED model captures volatility clustering and leverage effects, while EVT improves estimation of extreme losses. The combined GARCH–EVT framework better quantifies 1% tail risk than GARCH alone, directly addressing the research questions by (1) characterizing the nature and dynamics of interest rate risk, (2) demonstrating that GARCH–EVT minimizes underestimation of extreme VaR, and (3) informing policies to strengthen daily risk management and capital/liquidity planning in banks. These results suggest that extreme risk is non-negligible and that risk models must be updated dynamically with regime awareness to remain effective.

The study applies a two-stage framework—Markov regime switching and GARCH-family volatility modeling augmented with EVT—to O/N SHIBOR after China’s interest rate marketisation. The series displays sharp peaks, fat tails, volatility clustering, and leverage effects. AR(1)-EGARCH(1,1)-GED provides the best in-sample fit; EVT enhances extreme tail estimation. At the 99% confidence level, EVT-based VaR (≈0.6609%) is more conservative and better supported by backtests than GARCH-only VaR, while GARCH models perform comparatively better at higher tail probabilities (e.g., 10%). Backtesting validates model adequacy at 1% and 5% levels. Contributions include (i) documenting a volatility regime shift post-2018, (ii) identifying EGARCH-GED as a suitable model for O/N SHIBOR, and (iii) showing the superiority of GARCH–EVT for extreme risk quantification. Policy implications: Banks should (a) recognize persistent, regime-dependent volatility and incorporate GARCH–EVT into daily risk systems; (b) allocate sufficient liquidity buffers—results suggest maintaining >1% liquidity reserve in a reasonable window to absorb tail losses; (c) establish specialized pricing and interest rate risk management functions separate from product marketing; and (d) enhance training for staff on interest rate risk measurement and management. These steps can strengthen resilience under market-determined rates and support sustainable operations.

Future volatility dynamics are uncertain; model performance can degrade as regimes shift. Only selected GARCH specifications and two regimes were analyzed; multi-regime or long-memory models could be explored. The study focused on VaR; CVaR (expected shortfall) would better capture tail severity beyond VaR. Spillover/transmission from SHIBOR to banks’ product-level risks was not modeled and remains a direction for further research. Parameter labeling in EVT outputs may vary; broader sensitivity analyses on threshold selection and tail parameter stability could enhance robustness.